The global proof of the Polak–Ribière–Polak algorithm under the YWL inexact line search technique

This paper presents a new proof method about the paper (Yuan et al. in Appl. Math. Model. 47:811–825, 2017 ). In the proof, the global convergence of the Polak–Ribière–Polak algorithm is established without these two assumptions d k T g k < 0 and g k + 1 d k ≤ − σ 1 g k T d k which are needed in...

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Bibliographic Details
Published in:Journal of inequalities and applications 2019-07, Vol.2019 (1), p.1-13, Article 195
Main Authors: Li, Xiangrong, Yang, Tianshan, Wang, Xiaoliang
Format: Article
Language:English
Subjects:
Algorithms
Analysis
Applications of Mathematics
Global convergence
Mathematics
Mathematics and Statistics
Muskingum model
Nonconvex functions
PRP method
WWP line search
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Summary:This paper presents a new proof method about the paper (Yuan et al. in Appl. Math. Model. 47:811–825, 2017 ). In the proof, the global convergence of the Polak–Ribière–Polak algorithm is established without these two assumptions d k T g k < 0 and g k + 1 d k ≤ − σ 1 g k T d k which are needed in the above paper. This means that this paper has the same results under weaker conditions. More dimension functions for practical problems are tested to show the performance of the modified algorithm and the normal algorithm. An application of the fact engineering model is done to show the effectiveness of the given conjugate gradient algorithm.
ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/s13660-019-2148-x